Hint for Problem 11.2

If a set of points (x_i,y_i) is co-linear, then

A x_i + B y_i + C = 0 for some constants A, B, C.

This in turn implies, after multiplying by x_i, that

A x_i² + B y_ix_i + C x_i = 0 and after multiplying by y_i that A x_iy_i + B y_i² + C y_i = 0

These relationships imply that one can simplify a certain determinant. If enough elements vanish, than one can show the determinant is zero.